Ordinary Differential Equations
I. Course Prefix/Number: MAT 262
Course Name: Ordinary Differential Equations
Credits: 3 (3 lecture; 0 lab)
III. Course (Catalog) Description
IV. Learning Objectives
2. Solve linear differential equations by demonstrating the existence, uniqueness, and structure of solutions, including linear independence and its relationship to the Wronskian.
3. Solve linear differential equations with constant coefficients by the methods of variation of parameters and undetermined coefficients.
4. Solve linear systems of differential equations by the methods of elimination and eigenvalues.
5. Solve differential equations using Laplace transforms.
6. Solve differential equations using power series.
7. Solve differential equations using numerical methods, and classify the limitations of those methods.
8. Model and solve physical problems using methods presented in the course, including use of appropriate calculator and computer technology.
V. Academic Integrity
• plagiarism (turning in work not written by you, or lacking proper citation),
• falsification and fabrication (lying or distorting the truth),
• helping others to cheat,
• unauthorized changes on official documents,
• pretending to be someone else or having someone else pretend to be you,
• making or accepting bribes, special favors, or threats, and
• any other behavior that violates academic integrity.
There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.
Details of the Code of Academic Conduct can be found in the Student Handbook.
VI. Sequence of Topics
a. Linear equations
b. Separable equations
c. Exact equations
d. Integrating factors
e. Use of technology to solve differential equations and systems
2. Higher Order Linear Differential Equations
a. Homogeneous equations
b. Reduction methods for order of equations
c. Homogeneous equations with constant coefficients
d. Complex roots of auxiliary equations
e. Nonhomogeneous equations
f. Method of undetermined coefficients
g. Method of variation of parameters
h. Use of technology to support calculations
3. Applications and modeling
a. Growth and decay
d. Spring-mass systems
e. Electric circuits
f. Numerical techniques
4. Systems of differential equations
a. Elimination method
b. Eigenvalue method
c. Use of technology to demonstrate methods
5. Laplace transform
a. Properties of the Laplace transform
b. Inverse transform and solution of initial value problems
c. The Laplace transform of discontinuous functions
d. Convolutions calculated by the Laplace transform
e. Use of technology to calculate Laplace transforms
6. Power series
a. Power and Taylor series
b. Regular and ordinary singular points
c. Frobenius' method
VII. Methods of Instruction
Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Mathematica, Derive, and TI-92 Calculators are available for use at the College at no charge.
Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
IX. Instructional Materials
Textbook information for each course and section is available on Oakton’s Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words “View Book Information”.
A computer algebra system is required. Mathematica, Derive or use of a TI-89 or a TI-92 is recommended.
X. Methods of Evaluating Student Progress
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.
XI. Other Course Information
If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.